Do you understand Norwegian/Swedish/Danish? It is of course much better to
write an answere in norwegian but english no problem.
The Syagrus is not staying out during the winter. To protect a 4-5 meter tall palm
could be hard work. Besides, the Syagrus is said to be hardy to around -4/5 and in
Bergen it gets colder than that. But anything is possible with good
protection and I do not believe it's the cold that kills the palms
and other exotic plants, but the lenght of the period with low temps.
I have had plants surviving until feb/mar and then suddenly died
without any reason. The best tip I could give anyone growing exotics
plants is to simply put on a roof to protect the plants from rain.
Believe that this is important the first 2-3 years while the plants
and especially the palms are establishing their roots in the ground
and do not grow so much above the ground. A healthy palm with a good
established root system will take much more frost and cold than a
palm that have been damaged during the first years after planting.
By keeping the soil dry you will also increase the cold tolerance a lot
and this is of course important if you are growing arid plants (agave,
yucca, dasylirion, etc)

Many of the plants I bought in the UK this spring have not been through
their first winter yet, but for some of the other plants /palms I put on
a box with a bright plastic roof and three of the sides are covered with
felted material/cloth. One side open for good air circulation and I always
place the box with the open unprotected side away from the most wind exposed
direction. I our humid climate (and the lenght of the winter) it's not a
good solution to wrapp the plants/palms together (tie them up) and then
cover them because that will most probably cause them to start rot.
It's better to let to crown be open and to use some dry straw/gras/leaf for
protection inside the box. I also use styrofoam to protect the ground if that
should be necessary. My garden have many areas where the ground does not
get frozen during the winter and its also exposed to sun from early
morning until late evening.
But growing exotic plants is ALWAYS a challenge and my best tips might not
be the best ones for other parts of Scandinavia/North Europe.
I will take some photos of my protection later this year (December) to
show you how it works.